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3 years ago

Dave has a board that is 314 feet long. He cut off 178 feet from the board. How long is the remaining piece of board?

Mathematics

1 answer:

m_a_m_a [10]3 years ago

5 0

Answer:

314-178=136 the remainig piece of board is 136

Step-by-step explanation:

so first u subtract 314 with 178 becuase it said that he cut off so u subtract then after u subtract u get the answer 136

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It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel

Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

$speed = \frac{distance}{time}$

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

The total distance travelled by the train across the bridge is given by:

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 1260}{60}$

The total distance travelled by the train through the tunnel is given by:

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 2010}{90}$

The speed of the train was the same in both cases.

Equate both speeds

$\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}$

$\frac{x+630}{30} = \frac{x+1005}{45}$

$45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120$

Thus length of train is 120 meters

Find the speed of train:

$speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25$

Thus speed of train is 25 meter per second

5 0

3 years ago

2(4x - 3) 2-3(3x) + 5x

SashulF [63]

Answer:

12x-12

Step-by-step explanation:

I believe this is the correct answer, but correct me if I'm wrong.

7 0

3 years ago

Determine the kinetic energy of a 100-kg roller coaster car that is moving with a speed of 20.0/ms.

rjkz [21]

Answer:

The kinetic energy is 20,000\ J

Step-by-step explanation:

The kinetic energy of a body is defined as:

$k = \frac{1}{2}ms ^ 2$

Where m is the mass of the roller coaster car

s is the speed and k is the kinetic energy

We know that $s = 20\ m/s$

$m = 100\ kg$

Then the kinetic energy of the roller coaster car is:

$k = \frac{1}{2}(100)(20) ^ 2\\\\k = 50(20) ^ 2\\\\k = 50 * 400\\\\k = 20,000\ J$

3 0

3 years ago

For f(x)= x+5 and g(x)=4x+2 find (fog)(x) And (gof)(x)

Svetllana [295]

Composing functions means that the input of the outer functions is the output of the inner function.

In fact, you can rewrite the circle notation as

$(f\circ g)(x)=f(g(x)),\quad (g\circ f)(x)=g(f(x))$

So, we can substitute g(x) with its expression:

$(f\circ g)(x)=f(g(x))=f(4x+2)$

And since f(x)=x+5, we simply have to add 5 to its input:

$f(4x+2)=(4x+2)+5=4x+7$

Similarly, we have, substituting f with its expression,

$(g\circ f)(x)=g(f(x))=g(x+5)$

And since g(x)=4x+2, we have to multiply the input by 4 and add 2:

$g(x+5)=4(x+5)+2=4x+20+2=4x+22$

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3 years ago

Solve for x: 4x(3y-2)=7x+11

kupik [55]

Answer:

x=11(12y-15)

Step-by-step explanation:

4x(3y-2)=7x+11

12xy-8x=7x+11

12xy-8x-7x=11

12xy-15x=11

x(12y-15)=11

x(12y-15)/(12y-15)=11/(12y-15)

x=11/(12y-15)

7 0

3 years ago

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